Kuter is known for his role in the 1960s television series Green Acres and Petticoat Junction as Newt Kiley. He seesawed back and forth between both shows. Often he would appear with a hat on, looking like Pennsylvania senator Arlen Specter. He also starred in several television movies.
In recent years, Kay did extensive voice acting in video games including playing the bartender Griswold Goodsoup in The Curse of Monkey Island and Dockmaster Velasco in Grim Fandango, both well-known LucasArts Adventure games of the 90s. He was probably best known to video game fans as Werner Huber in Gabriel Knight: The Beast Within. He was also the voice of "Hershey's Kisses" commercials for 14 years.
He made guest appearances on many television shows including Bonanza, Perry Mason, Star Trek: The Next Generation as a Cytherian in the season 4 episode "The Nth Degree", and in Star Trek: Deep Space Nine as the Bajoran Sirah in the season 1 episode "The Storyteller". He also appeared on ER, Charmed, Seinfeld as the Latvian Orthodox priest, and Frasier as a vagrant who wants a kiss from Martin.